On a Bertrand Dynamic Game with Differentiated Goods, Heterogeneous Expectations and Asymmetric Cost Functions

Abstract

The aim of this paper is to study the dynamics of a nonlinear Bertrand-type duopoly game with differentiated goods, linear demand and asymmetric cost functions. The game is modeled with a system of two difference equations. Existence and stability of equilibrium of this system are studied. We show that the model gives more complex, chaotic and unpredictable trajectories as a consequence of change in the parameter of speed of adjustment, which is followed by the bounded rational player, and in the parameter of product differentiation. A higher (lower) degree of player’s adjustment destabilizes (stabilize) the economy. Also, a higher or lower degree of product differentiation destabilizes the economy. The chaotic features are justified numerically via computing Lyapunov numbers, sensitive dependence on initial conditions, bifurcation diagrams and strange attractors.